a) To find A ∩ C which is the intersection of sets A and C, we are looking for elements that are common to both sets. Set A is {1, 2, 3} and set C is {2, 3, 4}. Both these sets contain the numbers 2 and 3. Therefore, A ∩ C = {2, 3}.
b) A ∪ (C ∩ D) signifies the union of set A and the intersection of sets C and D. First, let's find the intersection of sets C and D. Set C is {2, 3, 4} and set D is {3, 4, 5}. The common elements to both sets are 3 and 4. Therefore, C ∩ D = {3, 4}. Now, for the union of set A and the intersection of sets C and D. Set A is {1, 2, 3} and C ∩ D = {3, 4}. We combine all elements from these sets together, without repeating any elements. Hence, A ∪ (C ∩ D) = {1, 2, 3, 4}.
c) A ∩ Dᶜ refers to the elements that are common in set A and the complement of set D. The complement of set D means every element that is not in set D, within the given range. According to the range of 1-5, and given set D is {3, 4, 5}, the complement of set D, Dᶜ = {1, 2}. Set A is {1, 2, 3}. The common element between A and Dᶜ is 1 and 2. Therefore, A ∩ Dᶜ = {1, 2}.
d) There is no event corresponding to "None of the above".